A Machine Learning Approach to Portfolio Risk Management
Risk measurement, valuation and hedging form an integral task in portfolio risk management for insurance companies and other financial institutions. Portfolio risk arises because the values of constituent assets and liabilities change over time in response to changes in the underlying risk factors. The quantification of this risk requires modeling the dynamic portfolio value process. This boils down to compute conditional expectations of future cash flows over long time horizons, e.g., up to 40 years and beyond, which is computationally challenging.
This
lecture
presents
a
framework
for
dynamic
portfolio
risk
management
in discrete
time
building
on
machine
learning
theory.
We
learn
the
replicating martingale
of
the
portfolio
from
a
finite
sample
of
its
terminal
cumulative
cash
flow. The
learned
replicating
martingale
is
in
closed
form
thanks
to
a
suitable
choice
of the
reproducing
kernel
Hilbert
space.
We
develop
an
asymptotic
theory
and
prove
convergence
and
a
central
limit
theorem.
We
also
derive
finite
sample
error
bounds and
concentration
inequalities.
As
application
we
compute
the
value
at
risk
and expected
shortfall
of
the
one-year
loss
of
some
stylized
portfolios.
DAMIR FILIPOVIC
Damir
Filipović
holds
the
wissquote
Chair
in
Quantitative
Finance
at
the
Ecole
Polytechnique
Fédérale
de
Lausanne
(EPFL)
and
a
Swiss
Finance Institute
Senior
Chair.
He
also
acts
as head
of
the
Swiss
Finance
Institute
at EPFL.
He holds a PhD in mathematics from ETH Zurich and has been a faculty member of the University of Vienna, the University of Munich and Princeton University. He also worked for the Swiss Federal Office of Private Insurance as co-developer of the Swiss Solvency Test.
He is on the editorial board of several academic journals. His research focus is in quantitative finance and risk management. His papers have been published in a variety of academic journals including the Journal of Finance, Journal of Financial Economics, Mathematical Finance, Finance and Stochastics, and the Annals of Applied Probability. He is the author of a textbook titled Term-Structure Models.
David A. Sprott (1930-2013)
Professor
David
Sprott
was
the
first
Chair
(1967-1975)
of
the
Department
of Statistics
and
Actuarial
Science
at
the
University
of
Waterloo
and
first
Dean
of
the Faculty
of
Mathematics
(1967-1972).
The
David
Sprott
Distinguished
Lecture
Series was
created
in
recognition
of
his
tremendous
leadership
at
a
formative
time
of
our
department,
as
well
as
his
highly
influential
research
in
statistical
science.